Three-dimensional turning simulation modeling method and system considering tool nose arc

Abstract

The invention provides a three-dimensional turning simulation modeling method and system considering a tool nose arc, and relates to the field of turning machining.The specific scheme comprises the steps that a tool with the tool nose arc and a complete workpiece model are established respectively, and initial assembly is conducted; according to the initial assembly result and the cutting edge type of the tool, the center position of a prefabricated groove is determined, and the prefabricated groove is formed in the complete workpiece model; the tool and the workpiece model with the prefabricated groove are reassembled, and a three-dimensional turning model is obtained after material attribute setting and mesh generation; after simulation conditions of the three-dimensional turning model are set, simulation is conducted on the turning process, and turning process data are obtained; according to the method, the groove is prefabricated in the workpiece, the area with the cutting thickness of 0 at the junction of the cutter and the workpiece is eliminated, and simulation errors caused by excessive distortion of grids in the area are avoided.

Description

Technical Field

[0001] The invention belongs to the field of turning processing, and in particular relates to a three-dimensional turning simulation modeling method and system taking tool tip arc into consideration. Background Art

[0002] The cutting process is a highly nonlinear force-heat coupling process. There is a complex interaction between the tool and the workpiece material in the contact area, which produces extremely high stress, strain and strain rate, which determines the tool wear and machining surface quality in the cutting process. However, due to the high cutting speed and the closed contact area between the tool and the workpiece, the actual temperature, strain, strain rate, etc. in the cutting zone are difficult to monitor in real time, which greatly hinders the development of cutting theory.

[0003] With the rapid development of computer simulation technology, simulation technology has become an important and effective means of theoretical research on cutting processing, which can help researchers obtain important information such as temperature, stress, strain and strain rate distribution in the cutting area. When considering the arc structure of the tool tip, a typical three-dimensional turning simulation model such as Figure 1 As shown in the figure, the dark part is the cut-off part of the workpiece. The thickness of the cut-off part in this model varies. The maximum thickness is the feed rate f, and the minimum thickness is 0 (the area marked by the red line in the figure). It is very easy to deform too much, which will cause the simulation to be interrupted and the turning process cannot be fully simulated. For Abaqus, Deform and AdvantEdge, three commonly used software in the current cutting simulation field, when running Figure 1 The three-dimensional turning simulation models shown in the figure all have their own problems when considering the tool nose arc.

[0004] Abaqus is the software with the highest degree of freedom among the three. Users can easily customize tool motion trajectory, workpiece material properties, cooling and heat dissipation conditions, etc. In addition to conventional turning, it can also simulate special cutting processes such as ultrasonic vibration cutting and cryogenic cutting in various dimensions. In terms of output results, conventional results such as cutting force, cutting temperature, and residual stress field can be obtained, and results such as grain size can also be obtained through secondary development. However, there are very few cases where Abaqus successfully runs a three-dimensional turning simulation model that takes into account the tool tip arc. According to the results in the literature, Professor Zhang Xueping of Shanghai Jiao Tong University used this model in the paper "Three-dimensional finite element simulation and experiment of high-speed dry cutting process", but did not explain the specific modeling method, and the model was not used in subsequent research; Oze l of Rutgers University in the United States introduced the experience of using adaptive grids to run the model in the paper "Numerical modelling of 3D hard turning using arbitrary Lagrangian Eulerian fine el ement method", but the error rate in actual use is still very high, especially in ultrasonic vibration-assisted cutting, the success rate is almost 0, and subsequent successful cases using this method have not been reported; therefore, the current Abaqus-based three-dimensional turning simulation is mostly limited to orthogonal turning, ignoring the tool tip arc radius; but this method cannot study the influence of parameters such as the tool main deflection angle, and the simulation results are quite different from the actual cutting experimental results.

[0005] The premise for Deform software to run a three-dimensional turning simulation model that takes into account the tool tip arc is to set the workpiece material to a plastic body and remove the material's elastic properties; this method has low simulation accuracy and cannot obtain the residual stress field of the machined surface.

[0006] AdvantEdge software can directly run the three-dimensional turning simulation model that takes into account the tool tip arc, with a very high success rate, and can also obtain conventional results such as cutting force and cutting temperature; however, the developability of AdvantEdge software is poor, and it is impossible to obtain complete residual stress fields, grain size and other results through development. In addition, ultrasonic vibration cannot be applied to the tool in the three-dimensional turning simulation, and simulation research on processes such as ultrasonic vibration-assisted turning cannot be carried out.

[0007] Therefore, the existing turning simulation modeling technology has great limitations when performing three-dimensional turning simulation considering the tool tip arc, and it is difficult to efficiently carry out accurate simulation of new turning methods such as ultrasonic vibration cutting and obtain turning process data. Summary of the invention

[0008] In order to overcome the shortcomings of the above-mentioned prior art, the present invention provides a three-dimensional turning simulation modeling method and system taking into account the arc of the tool tip. By prefabricating grooves on the workpiece, the area with zero cutting thickness at the junction of the tool and the workpiece is eliminated, thereby avoiding distortion and errors of the grid in this area.

[0009] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:

[0010] A first aspect of the present invention provides a three-dimensional turning simulation modeling method taking into account tool tip arc.

[0011] A three-dimensional turning simulation modeling method considering tool tip arc, comprising:

[0012] Establish the tool with tool tip arc and the complete workpiece model respectively, and perform initial assembly;

[0013] According to the initial assembly result and the cutting edge type of the tool, the center position of the prefabricated groove is determined, and the prefabricated groove is opened on the complete workpiece model;

[0014] After reassembling the tool and opening the prefabricated groove, the workpiece model is obtained after material property setting and meshing;

[0015] After setting the simulation conditions of the three-dimensional turning model, the turning process is simulated to obtain the turning process data.

[0016] Furthermore, the initial assembly is to assemble the tool and the workpiece model according to the set feed rate and cutting depth.

[0017] Furthermore, the determining of the center position of the prefabricated groove is specifically as follows:

[0018] For the model without considering the bluntness of the cutting edge, the intersection of the tool cutting edge and the workpiece transition surface is taken as the width center of the prefabricated groove;

[0019] For the model considering the bluntness of the cutting edge, the intersection of the bluntness boundary of the cutting edge on the rake face of the tool and the transition surface of the workpiece is taken as the width center of the prefabricated groove;

[0020] For the conventional vibration-free turning model, the width and depth of the prefabricated grooves were reduced to improve the simulation accuracy, both of which were set to 1 to 2 times the grid size;

[0021] For the ultrasonic vibration-assisted turning model, the width of the prefabricated groove needs to be widened to ensure that the intersection of the blunt edge boundary of the cutting edge on the tool rake face and the workpiece transition surface is always within the prefabricated groove during tool vibration, and the groove depth is set to 1 to 2 times the grid size.

[0022] Furthermore, it also includes using Solidworks software for modeling and using Abaqus software for simulation.

[0023] Furthermore, the meshing is to appropriately divide the imported workpiece with prefabricated grooves, and to mesh the tool model and the workpiece model respectively.

[0024] Furthermore, the simulation conditions of setting the three-dimensional turning model include:

[0025] Set the contact properties between the workpiece model and the tool model;

[0026] Create analysis steps according to cutting motion characteristics and set appropriate mass scaling factors;

[0027] Set boundary conditions on the workpiece and apply motion loads to the tool.

[0028] Furthermore, the turning process data includes cutting force, cutting temperature, residual stress field, and grain size.

[0029] A second aspect of the present invention provides a three-dimensional turning simulation modeling system that takes tool tip arc into consideration.

[0030] A three-dimensional turning simulation modeling system considering tool tip arc includes an initial assembly module, a groove opening module, a reassembly module and a simulation module:

[0031] The initial assembly module is configured to: respectively establish a tool with a tool tip arc and a complete workpiece model, and perform initial assembly;

[0032] The groove opening module is configured to: determine the center position of the prefabricated groove according to the initial assembly result and the cutting edge type of the tool, and open the prefabricated groove on the complete workpiece model;

[0033] The reassembly module is configured to: reassemble the tool and the workpiece model after the prefabricated groove is opened, and obtain a three-dimensional turning model after material property setting and meshing;

[0034] The simulation module is configured to: after setting the simulation conditions of the three-dimensional turning model, simulate the turning process to obtain the turning process data.

[0035] The third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps of a three-dimensional turning simulation modeling method taking into account a tool tip arc as described in the first aspect of the present invention.

[0036] The fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, the steps in a three-dimensional turning simulation modeling method taking into account the tool tip arc as described in the first aspect of the present invention are implemented.

[0037] One or more of the above technical solutions have the following beneficial effects:

[0038] The present invention solves the problem that the simulation model cannot run due to grid distortion and error reporting by prefabricating grooves in the area where the cutting thickness is zero at the junction of the tool and the workpiece. It can be used for multi-dimensional ultrasonic vibration-assisted turning process simulation, tool geometry optimization simulation research, etc., providing conditions for scientific research in the field of turning processing.

[0039] The three-dimensional turning simulation model based on Abaqus and considering the tool tip arc established in the present invention retains the high degree of freedom of the Abaqus model and has a wide range of applications. It can freely define the tool geometry, cutting angle, motion trajectory, workpiece material properties, cooling and heat dissipation conditions, etc. In addition to conventional turning, it can also simulate special cutting processes such as ultrasonic vibration cutting and cryogenic cutting in various dimensions. In terms of output results, conventional results such as cutting force, cutting temperature, residual stress field, etc. can be obtained, and results such as grain size can also be obtained through secondary development.

[0040] The model established by the present invention does not require special processing of the grid type, size, division method, etc., nor does it need to simplify the workpiece material properties. The modeling process is simple, the operation success rate is high, and the simulation accuracy is high.

[0041] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0043] Figure 1 Schematic diagram of the three-dimensional turning simulation model considering the tool tip arc.

[0044] Figure 2 This is a flow chart of the method of the first embodiment.

[0045] Figure 3 It is a schematic diagram of the three-dimensional turning simulation model with tool tip arc without considering the bluntness of the cutting edge in the first embodiment.

[0046] Figure 4 This is a schematic diagram of a three-dimensional turning simulation model with a tool tip arc and a blunt cutting edge for the first embodiment.

[0047] Among them, 1-tool, 1-1-cutting edge, 1-2-cutting edge bluntness, 1-3-cutting edge bluntness boundary on the front cutting face, 2-workpiece, 2-1-machined surface, 2-2-transition surface, 2-3-surface to be machined, 3-prefabricated groove. DETAILED DESCRIPTION

[0048] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0049] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0050] In response to the simulation needs of new cutting process such as ultrasonic vibration assisted turning, the present invention innovatively proposes a modeling method for prefabricating grooves in the area with cutting thickness of 0 at the junction of the tool and the workpiece based on the analysis of the interruption causes of the three-dimensional turning simulation model considering the tool tip arc. The method solves the problem of the simulation model being unable to run due to mesh distortion and error without significantly reducing the simulation accuracy, and establishes a reliable three-dimensional turning simulation model considering the tool tip arc.

[0051] Embodiment 1

[0052] In one embodiment of the present disclosure, a three-dimensional turning simulation modeling method considering tool tip arc is provided. Figure 2 As shown, the following steps are included:

[0053] Step 1: Establish the tool with tool tip arc and the complete workpiece model respectively, and perform initial assembly;

[0054] Step 2: According to the initial assembly results and the cutting edge type of the tool, determine the center position of the prefabricated groove and open the prefabricated groove on the complete workpiece model;

[0055] Step 3: Reassemble the tool and the workpiece model after the prefabricated groove is opened, and after setting the material properties and meshing, a three-dimensional turning model is obtained;

[0056] Step 4: After setting the simulation conditions of the 3D turning model, simulate the turning process to obtain the turning process data.

[0057] Furthermore, the initial assembly is to assemble the tool and the workpiece model according to the set feed rate and cutting depth.

[0058] Furthermore, the determining of the center position of the prefabricated groove is specifically as follows:

[0059] For the model without considering the bluntness of the cutting edge, the intersection of the tool cutting edge and the workpiece transition surface is taken as the width center of the prefabricated groove;

[0060] For the model considering the bluntness of the cutting edge, the intersection of the bluntness boundary of the cutting edge on the rake face of the tool and the transition surface of the workpiece is taken as the width center of the prefabricated groove;

[0061] For the conventional vibration-free turning model, the width and depth of the prefabricated grooves were reduced to improve the simulation accuracy, both of which were set to 1 to 2 times the grid size;

[0062] For the ultrasonic vibration-assisted turning model, the width of the prefabricated groove needs to be widened to ensure that the intersection of the blunt edge boundary of the cutting edge on the tool rake face and the workpiece transition surface is always within the prefabricated groove during tool vibration, and the groove depth is set to 1 to 2 times the grid size.

[0063] Furthermore, it also includes using Solidworks software for modeling and using Abaqus software for simulation.

[0064] Furthermore, the meshing is to appropriately divide the imported workpiece with prefabricated grooves, and to mesh the tool model and the workpiece model respectively.

[0065] Furthermore, the simulation conditions of setting the three-dimensional turning model include:

[0066] Set the contact properties between the workpiece model and the tool model;

[0067] Create analysis steps according to cutting motion characteristics and set appropriate mass scaling factors;

[0068] Set boundary conditions on the workpiece and apply motion loads to the tool.

[0069] Furthermore, the turning process data includes cutting force, cutting temperature, residual stress field, and grain size.

[0070] The following is a detailed description of the implementation process of a three-dimensional turning simulation modeling method taking into account the tool tip arc in this embodiment.

[0071] This embodiment provides a three-dimensional turning simulation model modeling method based on Abaqus considering the tool tip arc, which provides conditions for scientific research in the field of cutting processing. The specific steps are as follows:

[0072] Step S1, using modeling software such as Solidworks to establish a tool with a tool tip arc and a complete workpiece model;

[0073] Step S2, assembling the tool and the workpiece model according to the set feed rate and cutting depth;

[0074] Step S3, after determining the center position of the prefabricated groove according to the assembly result and the type of the tool cutting edge, returning to the workpiece model module, and opening the prefabricated groove on the complete workpiece model;

[0075] The method for determining the center position of the prefabricated groove is:

[0076] (1) For the model without considering the bluntness of the cutting edge, the intersection of the tool cutting edge and the workpiece transition surface is the width center of the prefabricated groove;

[0077] Specifically, Figure 3 As shown, the center of the width direction of the prefabricated groove 3 is located at the intersection of the cutting edge 1-1 of the tool 1 and the transition surface 2-2 of the workpiece 2 ( Figure 3 Indicated by the red dot in the middle.

[0078] (2) For the model considering the bluntness of the cutting edge, the intersection of the bluntness boundary of the cutting edge on the rake face of the tool and the transition surface of the workpiece is the width center of the prefabricated groove;

[0079] Specifically, Figure 4 As shown, the center of the width direction of the prefabricated groove 3 is located at the intersection of the boundary 1-3 of the blunt circle 1-2 of the cutting edge on the rake face of the tool 1 and the transition surface 2-2 of the workpiece 2 ( Figure 4 Indicated by the red dot in the middle.

[0080] (3) For conventional vibration-free turning models, the width and depth of the prefabricated grooves should be minimized to improve simulation accuracy, and are generally set to 1 to 2 times the grid size;

[0081] (4) For the ultrasonic vibration-assisted turning model, the width of the prefabricated groove needs to be appropriately widened to ensure that the intersection of the blunt edge boundary of the cutting edge on the tool rake face and the workpiece transition surface is always within the prefabricated groove during tool vibration. The groove depth can generally be set to 1 to 2 times the grid size.

[0082] Step S4, reassemble the tool and workpiece model, save them as Parasolid type and import them into the Abaqus assembly module;

[0083] Step S5, assigning material properties to the imported tool model and workpiece model respectively through Abaqus simulation software;

[0084] Step S6, appropriately segmenting the imported workpiece with prefabricated grooves through the mesh module in the Abaqus simulation software, and meshing the tool model and the workpiece model respectively;

[0085] Step S7, setting the contact properties between the workpiece model and the tool model, friction coefficient, heat transfer coefficient, etc.;

[0086] Step S8, creating an analysis step according to the cutting motion characteristics and setting a suitable mass scaling factor;

[0087] Step S9, setting boundary conditions for the workpiece and applying motion load to the tool through the load module in the Abaqus software;

[0088] Step S10, submitting the three-dimensional turning model considering the tool tip arc processed by steps S1-S6 to the solver of Abaqus simulation software for solving and running to obtain the running result.

[0089] This method solves the problem of the simulation model being unable to run due to mesh distortion and errors by prefabricating grooves in the area with zero cutting thickness at the junction of the tool and the workpiece. It can be used for multi-dimensional ultrasonic vibration-assisted turning process simulation, tool geometry optimization simulation research, etc., providing conditions for scientific research in the field of turning processing.

[0090] This embodiment verifies the effect of the method through experiments. The cutting speed of the ultrasonic vibration turning experiment of Ti6Al4V titanium alloy is 30m / min, the feed rate is 0.1mm / rev, and the cutting depth is 0.1mm; the ultrasonic vibration direction is the speed and cutting depth direction, the amplitude is 4.6μm and 5μm respectively, the frequency is 39.35kHz, and the phase difference is 90°; the radius of the tool tip arc is 0.4mm, and after the tool is installed on the ultrasonic amplitude rod, the front angle γ0, the back angle α0 and the blade inclination angle K r They are 0°, 7° and 5° respectively; the experiment was carried out under minimal lubrication conditions, using palm oil as the lubricating medium, the flow rate was fixed at 60ml / h, and the gas pressure was 0.7MPa; the main cutting force and cutting depth resistance measured by YDC-III89B piezoelectric dynamometer were 35.89N and 55.58N respectively.

[0091] A three-dimensional turning simulation model was established by the method of this embodiment to simulate the above experimental process. The cutting amount, tool geometry angle and ultrasonic vibration parameters were the same as those in the experimental process. The workpiece material properties were set according to the parameters in Wang Qingqing's paper "Evolutions of grain size and micro-hardness during chipformation and machined surface generation for Ti-6Al-4Vin high-speed machining", and the thermal conductivity was set to 0.1721W / m·K; the main cutting force and cutting depth resistance obtained by simulation were 39.06N and 48.17N, respectively, with errors of 8.83% and 13.33%, respectively, both lower than 15%, and the simulation accuracy met the conventional requirements of cutting simulation.

[0092] Embodiment 2

[0093] In one embodiment of the present disclosure, a three-dimensional turning simulation modeling system considering tool tip arc is provided, including an initial assembly module, a groove opening module, a reassembly module and a simulation module:

[0094] The initial assembly module is configured to: respectively establish a tool with a tool tip arc and a complete workpiece model, and perform initial assembly;

[0095] The groove opening module is configured to: determine the center position of the prefabricated groove according to the initial assembly result and the cutting edge type of the tool, and open the prefabricated groove on the complete workpiece model;

[0096] The reassembly module is configured to: reassemble the tool and the workpiece model after the prefabricated groove is opened, and obtain a three-dimensional turning model after material property setting and meshing;

[0097] The simulation module is configured to: after setting the simulation conditions of the three-dimensional turning model, simulate the turning process to obtain the turning process data.

[0098] Embodiment 3

[0099] The purpose of this embodiment is to provide a computer-readable storage medium.

[0100] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of a three-dimensional turning simulation modeling method taking into account a tool tip arc as described in the first embodiment of the present disclosure.

[0101] Embodiment 4

[0102] The purpose of this embodiment is to provide an electronic device.

[0103] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, the steps in a three-dimensional turning simulation modeling method taking into account a tool tip arc as described in the first embodiment of the present disclosure are implemented.

[0104] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A three-dimensional turning simulation modeling method considering tool tip arc, characterized in that: include: Establish the tool with tool tip arc and the complete workpiece model respectively, and perform initial assembly; According to the initial assembly result and the cutting edge type of the tool, the center position of the prefabricated groove is determined, and the prefabricated groove is opened on the complete workpiece model; After reassembling the tool and opening the prefabricated groove, the workpiece model is obtained after material property setting and meshing; After setting the simulation conditions of the three-dimensional turning model, the turning process is simulated to obtain the turning process data.

2. A three-dimensional turning simulation modeling method considering tool tip arc as claimed in claim 1, characterized in that: The initial assembly is to assemble the tool and the workpiece model according to the set feed rate and cutting depth.

3. A three-dimensional turning simulation modeling method considering tool tip arc as claimed in claim 1, characterized in that: The method of determining the center position of the prefabricated groove is specifically as follows: For the model without considering the bluntness of the cutting edge, the intersection of the tool cutting edge and the workpiece transition surface is taken as the width center of the prefabricated groove; For the model considering the bluntness of the cutting edge, the intersection of the bluntness boundary of the cutting edge on the rake face of the tool and the transition surface of the workpiece is taken as the width center of the prefabricated groove; For the conventional vibration-free turning model, the width and depth of the prefabricated grooves were reduced to improve the simulation accuracy, both of which were set to 1 to 2 times the grid size; For the ultrasonic vibration-assisted turning model, the width of the prefabricated groove needs to be widened to ensure that the intersection of the blunt edge boundary of the cutting edge on the tool rake face and the workpiece transition surface is always within the prefabricated groove during tool vibration, and the groove depth is set to 1 to 2 times the grid size.

4. A three-dimensional turning simulation modeling method considering tool tip arc as claimed in claim 1, characterized in that: It also includes modeling using Solidworks software and simulation using Abaqus software.

5. A three-dimensional turning simulation modeling method considering tool tip arc as claimed in claim 1, characterized in that: The meshing is to appropriately divide the imported workpiece with prefabricated grooves, and to mesh the tool model and the workpiece model respectively.

6. A three-dimensional turning simulation modeling method considering tool tip arc as claimed in claim 1, characterized in that: The simulation conditions for setting the three-dimensional turning model include: Set the contact properties between the workpiece model and the tool model; Create analysis steps according to cutting motion characteristics and set appropriate mass scaling factors; Set boundary conditions on the workpiece and apply motion loads to the tool.

7. A three-dimensional turning simulation modeling method considering tool tip arc as claimed in claim 1, characterized in that: The turning process data include cutting force, cutting temperature, residual stress field, and grain size.

8. A three-dimensional turning simulation modeling system considering tool tip arc, characterized in that: Including initial assembly module, groove opening module, reassembly module and simulation module: The initial assembly module is configured to: respectively establish a tool with a tool tip arc and a complete workpiece model, and perform initial assembly; The groove opening module is configured to: determine the center position of the prefabricated groove according to the initial assembly result and the cutting edge type of the tool, and open the prefabricated groove on the complete workpiece model; The reassembly module is configured to: reassemble the tool and the workpiece model after the prefabricated groove is opened, and obtain a three-dimensional turning model after material property setting and meshing; The simulation module is configured to: after setting the simulation conditions of the three-dimensional turning model, simulate the turning process to obtain the turning process data.

9. An electronic device, comprising: a memory for non-transitory storage of computer readable instructions; a processor for executing the computer-readable instructions; Wherein, when the computer-readable instructions are executed by the processor, the method according to any one of claims 1 to 7 is executed.

10. A storage medium, characterized in that: The computer-readable instructions are non-transitorily stored, wherein when the computer-readable instructions are executed by a computer, the method of any one of claims 1 to 7 is performed.

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